Remote controlled miniature 3 frequencies generator

I am taking an electronics design class and we have a product-development project that is described below. I am trying to figure out how to go about it. The tricky part is the size of it. The frequency generation part has to be able to fit in about a matchbox and I have to spec out the parts required to built it.

Basically I need to be able to generate 3 different frequencies that are 5Vpp with 0.01-0.03mA. All 3 frequencies need to be independent of each other, meaning each one can be turned on/off irrelevant of the state of the others.

Example, all can run at the same time, or just 2 can run at the same time or any combination, etc. The circuit needs to be able to fit in a matchbox, be able to run for 60 mins and can be controlled in a very simple way from a remote control. I think the remote can be made to have simply 3 buttons , one for each frequency, where each button turns each frequency on or off.
Attached is also a small conceptual diagram that I came up with... Of course there might be other and more efficient or simple ways to do this ...Please advice! What is the simplest and smallest way built this? I will need to built a functional prototype of this by the end of the month.

The remote control can be purchased separately or at least a configurable version of it, the integration of the receiver part to the circuit i need to figure out. I am thinking of using a 5Volt Lithium-Ion battery as a power supply. For the frequency generating part, from researching, I think 3 XR2206CP chips could do...